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G. Lippmann "Relations entre les phenomenes electriques et capillaries", Ann. chim. phys. (5), 5, 494 (1875) G. Gouy "Sur la fonction electrocapillaire I", Ann. chim. phys. (7), 29, 145 (1903) G. Gouy "Sur la fonction electrocapillaire II", Ann. chim. phys. (8), 8, 291 (1906) G. Gouy "Sur la fonction electrocapillaire III", Ann. chim. phys. (8), 9, 75 (1906) A. Frumkin "Zur Theorie der Elektrokapillaritat. I.", Ztschr. phys. Chem.,103, 43 (1923) A. Frumkin "Zur Theorie der Elektrokapillaritat. II.", Ztschr. phys. Chem.,103, 55 (1923)
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c = exp(-2a) 1-

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q = q0 (1 - ) + C1 ( - N )
C = 0 (1 - )

C =1

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Electrocapillary curves of a mercury electrode in 1M NaCl solutions containing tret-pentanol additives: 1 - 0; 2 - 0.01; 3 -0.05; 4 - 0.1; 5 - 0.2; 6 - 0.4 M

Experimental data

Calculated

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Experimental and simulated differential capacity curves, a=const

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Experimental and simulated differential capacity curves: linear a, E - dependence

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1 / C = 1 / C02 + 1 / C 2

= 02 + 2

2 C 2 = ( F / 2 RT ) 4 Ad x + q 2

q 2 RT arcsh 2 = 2A x F d

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Models of two parallel capacitors taking into account diffuse part of the electrical double layer
C 0 (1 - )

C

dif

C1
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Coadsorption of two solution components. Combination of two mixed Frumkin isotherms

= 0 (1-1 -2 ) + C11(E0 - EN1) + C22 (E0 - EN2 )
1 1c1 = n1 (1 - 1 -
2

)
2

n1

exp ( -2n1a111 - 2n1a12

2

) )
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2 2 c2 = n2 (1 - 1 -

)

n2

exp ( -2n2 a22 2 - 2n2 a121


2 , 1 relartionships corresponding to two equations
of mixed Frumkin isotherms

A, B, C, G ­ minimum; F ­ maximum; D, E ­ saddle point

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Models of two and three parallel capacitors taking into account diffuse part of the electrical double layer
C 0 (1 - )
Cdif

C0(1-1-2)

C1

C
1

dif

C1

C2

2

1

2
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mc TlNO3 + (1-m) c KNO3 at m : 1 ­ 0 , 2 ­ 0.02 , 3 ­ 0.05 , 4 ­ 0.1 , 5 - 0.2
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,

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q d = -QdE r - d H F

+

E r = C C d.l. = - FC + 0.058 H Q
q C d.l. = E r i ,

E r pH , Q
.
H+

H+

Q ;C = E r i ,

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(equilibrium charging curves)

Chronopotentiometry

Adsorption curves
Qt - E (RHE)
AH - E (RHE )

Equilibrium CV Isoelectric shifts of potential Potentiometric titration under isoelectric conditions
Qt Ct = E ( RHE )

q f - E (RHE )

Ct - E ( RHE )

E

E
ptzc

Radiotracer measurements + , - - E (RHE )
pfzc

High-frequency impedance

CO adsorption
q f Cf = E (RHE)

C f - E (RHE )

H+

H+

E ( RHE) = + H

CA = const Qt = q f - AH
C
CA t

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Points of zero charge - pH dependence

E
E H
+

pfzc

= qf =0 1 - ( q

f

1 AH

)

E ( RHE )

E
E H
Glass electrode Pt/Pt

ptzc

+

1 = Qt =0 1 - ( q f AH )

H+

Potentiometric titration under isoelectric conditions, 1974

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6 5 4

E (NHE)

pH

br om ide

1

su lfa te

2

ch lo r id e

3

0 0,10

(110)
0,15

(111)???
0,20

(100) (111)
0,30 0,35

ptzc:

0,25

E (RHE)
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0,40


2008

: !

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pzc

Cs+ Rb
+

S2O + 2e = 2SO
28 -

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K

+

Na+ Li
+

1953

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­

RT (ln - ln i ) - z 0 F1 =

F ( - 1 ) +; 2 2
630

RT (ln - ln i ) - z 0 F1 versus - 1

[H2CeW 10O36]


CTP (1963)
Cs
+

CMP (2006)
K
+

Na

+

Na

+

Li

+

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